polynomials

[deleeuw@galton.math.ucla.edu (Jan Deleeuw)]

Hello,

I am translating (part of) Stephen Moshier's Cephes Library from C to
CL. Since a lot of this is polynomial approximation, I need a really
efficient version of (poly x y) which implements Horner's rule. Here
x is the argument of the polynomial, and y is a list or vector of
coefficients (4-10 double-floats). I dont want to use assembler, because
of portability (yet). Some questions:
(a) Is there such code -- I have CL Math, but that seems tentative.
(b) Do I use a list or vector of coefficients.
(c) Is it advantageous to defconstant the coefficients, or do I just
pass the actual values to poly.
(d) Where do I put the declarations.

This is what I use now (from CL Math, but not using a macro)

(defun poly (var coefs)
(declare (double-float var) (type (list double-float *) coefs)
         (optimize (safety 0) (space 0) (speed 3)))
(cond ((null coefs) 0.0)
      ((null (cdr coefs)) (car coefs))
      (t (the double-float (+ (the double-float (car coefs))
         (the double-float (* (the double-float var) 
                              (the double-float (poly var (cdr coefs))))))))))

and here is an example of a function using poly

(defun stirf (x)
(declare (double-float x))
(let* (
      (a (/ x))
      (w (+ 1.0 (* a (poly a '(8.33333333333482257126e-2
                               3.47222221605458667310e-3
                              -2.68132617805781232825e-3
                              -2.29549961613378126380e-4
                               7.87311395793093628397e-4)))))
      (y (exp x))
      )
  (declare (double-float a w y))
(if (> x 143.01608) 
  (let* (
        (v (expt x (- 0.25 (* 0.5 x))))
        (r (* v (/ v y)))
        )
    (declare (double-float v r))
    (* w r 2.50662827463100050242e0))
  (let (
        (r (/ (expt x (- x 0.5)) y))
        )
    (declare (double-float r))
    (* w r 2.50662827463100050242e0)))
))

All suggestions are welcome.
The stronger the criticism, the more welcome it is.

--- Jan

Jan de Leeuw; Dept Math UCLA; phone (310)-825-9550; fax (310)-206-6673      
mail: 405 Hilgard Ave, Los Angeles, CA 90024-1555
INTERNET: deleeuw@laplace.stat.ucla.edu  

--
Jan de Leeuw; Dept Math UCLA; phone (310)-825-9550; fax (310)-206-6673      
mail: 405 Hilgard Ave, Los Angeles, CA 90024-1555
INTERNET: deleeuw@laplace.stat.ucla.edu